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U. S. SANITARY COMMISSION. 
STATISTICAL BUREAU. 



AGES 



OF 



U. S. VOLUNTEER SOLDIERY. 



NEW YORK 
1866. 






University Press : Welch, Bigelow, & Co., 
Cambridge. 



Cambridge, January, 1866. 

Dear Sir, — 

Inclosed is my Report on the Ages of Volunteers in the late war. 
The general results were communicated, by permission, to the 
National Academy of Sciences at its session in August last, and 
tins Report was read before the Commission in November ; but 
the Appendix, concerning the Ages of a Population in general, 
has been prepared since that time. 

For most of the troops comprised within the limits of the 
present discussion, no descriptive muster-rolls exist. The Ages, 
Nativities, and Statures of those troops whose descriptions are 
on record will soon be made the subject of another Report. 

I am, dear Sir, 

Very respectfully and sincerely yours, 

B. A. GOULD, 

Actuary U. S. Sanitary Commission. 

John S. Blatchford, Esq., 

General Secretary U. S. Sanitary Commission. 



CORRIGENDA. 

Pa<rc 6, line 23, for face read force. 

" 10, " 19, " 28.4843 " 28.4850. 

" 30, " 28, " Column 9 " Column 3. 

39, " 24, " one million •' one hundred thousand. 



AGES 



UNITED STATES VOLUNTEER SOLDIERY 



1. Introductory. 



On taking charge of the Statistical Department of the United 
States Sanitary Commission, in August, 1864, it was found that 
considerable progress had been made in collecting the ages of the 
soldiers of our volunteer regiments, — an investigation which had 
been suggested and commenced by Mr. Elliott, the accomplished 
and skilful statistician, who, not very long before, had relin- 
quished the direction of this Bureau of the Commission. 

Although the best use to be made of the materials appeared 
somewhat uncertain, it did not seem proper to discontinue in- 
quiries already so far advanced ; and the large experience of Mr. 
Elliott in matters connected with vital statistics gave assurance 
that valuable as well as interesting results were likely to be 
deduced from a thorough study of these data. 

The collection of these materials was therefore continued and 
completed, by means of the muster-rolls on file at the War De- 
partment in Washington, to which access was courteously af- 
forded by General E. D. Townsend, Acting Adjutant-General, and 
Colonel Samuel Breck, who was in charge of the rolls. Tables 
have thus been formed for twenty-seven States, Territories, or geo- 
graphical groups, exhibiting the number of men at each year 
of age in the volunteer organizations, at the time of their mus- 
ter into the service of the United States. The officers are tabu- 
lated as a distinct class ; and the three arms of the military 
service — infantry, cavalry, and artillery — have been treated 
separately. 



Z AGES OF VOLUNTEERS. 

The original collection of the materials was principally made 
by Mr. T. J. O'Connell, until lately the efficient and accurate 
chief clerk of the Statistical Department, and was completed by 
Mr. E. A. Wilson. The tabulation has been made by Messrs. 
O'Connell, Wilson, A. A. Brooke, and John N. Stockwell; 
and the greater part of the computations has been performed 
by Mr. Stockwell alone, with great care, perseverance, and 
ability. 

The recruits who joined these original regiments after their 
first organization and acceptance into the national service are 
not included ; and the limits of the investigation have excluded 
all drafted men, substitutes, &c. Moreover, many regiments be- 
longing within these limits are omitted, because organized since 
the collection of the data for the States to which they belong ; 
but the number of these is comparatively small, and inadequate 
to exert any sensible effect upon the results. The degree of com- 
pleteness may be seen by the following table, which shows the 
number and date of the latest regiment included in the collection. 



Arkansas 


2d Infantry, 


latest. 


Mississippi 


Marine Brig. 


only organ'n 


California 


4th 


tt 


1862, Feh. 


Missouri 


34th Infantry 


1862, Dec. 


Connecticut 


28th 


" 


1862, Nov. 


Nevada 


1st 


" 


1864, June 


Delaware 


2d 


" 


1861, Dec. 


N. Hampshire 1 8th 


" 


1864, Sept 


Illinois 


131st 


" 


1864, June. 


New Jersey 


25th 


u 


1862, Sept 


Indiana 


115th 


a 


1863, Aug. 


N. Mexico 


4th 


" 


1863. 


Iowa 


48th 


tt 


1865. 


New York 


177th 


" 


1863, June. 


Kansas 


15th 


" 


1863. 


Ohio 


128th 


" 


1863, Aug. 


Kentucky 


52d 


" 


1864. 


Pennsylvania 


t 155th 


" 


1863, Jan. 


Louisiana 


N. 0. 


Vols. 


1864, May. 


Rhode Island 12th 


" 


1862, Oct. 


Maine 


28th Infantry 


1864. 


Tennessee 


8th 


" 


1864. 


Maryland 


10th 


" 


1864, June. 


Vermont 


16th 


" 


1862, Oct. 


Mass. 


59th 


" 


1864, July. 


W. Virginia 


15th 


" 


1862, Sept. 


Michigan 


27th 


" 


1864, Aug. 


Wash. Terr. 


1st 


tt 


only reg't. 


Minnesota 


10th 


" 


1864, Aug. 


Wisconsin 


53d 


<t 


1864. 



The total number of volunteers whose ages have thus been 
investigated is 1 049 457, of whom 1 012 273 were enlisted men, 
and 37 184 were commissioned officers. All except 1^ per cen- 
tum (.01495) of the men, and 31 per centum (.0331) of the offi- 
cers, were between the ages of 18 and 46 years at the date of 
their enlistment or commission. Those beyond these limits have 
not been included in the determination of the general formulas, 



AGES OF VOLUNTEERS. 3 

so that these depend upon the statistics of ages for 1 032 600 men, 
of whom 35 953 were commissioned officers.* 

The results have proved amenable to law in a higher degree 
than I had ventured to anticipate. Residual discordances exist, 
of course, between the numbers for each year of age, as derived 
from the tabulated records, and those indicated by the general 
formulas deduced from the whole series ; yet where these dis- 
cordances attain any essential magnitude, they may almost in- 
variably be made to yield instructive and useful information. 

The results attained, for that portion of the population who 
thus rushed to the field at their country's call, naturally suggest 
analogous inquiries regarding the white male population of the 
United States, and especially relative to the population of that 
portion of the country which furnished the volunteers under con- 
sideration. And it was not until after many unavailing efforts 
to obtain information as to the distribution of our population by 
ages, that the great deficiency of our knowledge of the facts and 
laws relative to this very important subject became manifest. 

The only published attempt, of which I am aware, to classify the 
population of the United States according to years of age is very 
crude, and the method pursued yields results quite at variance 
from the truth. The only trustworthy facts are contained in the 
summaries of the census-returns ; and the groups into which the 
population is there divided are altogether too large to permit the 
desired laws to be deduced with ease. It is earnestly to be hoped 
that in future census-publications the groups may be so made as 
to include intervals of age not greater than five years. 

It thus became important, if only for the sake of comparison 
between the age%of the volunteer troops and that of the popula- 
tion whence they sprung, to subject the census of 1860 to a simi- 
lar discussion. And I cannot but think that the results elicited 
might be advantageously employed, so far as they apply and 
extend, for the life-tables of our insurance and annuity offices. 
The life-curve for our American population is clearly diverse 
from the curve on which the present English tables are based ; 

* The prescribed limits of military age at the commencement of the rebellion were 
18 and 45 years ; but the large proportional number at the age of 45 seems to indicate 
that the law was so interpreted as to permit the acceptance of volunteers whose age at 
their last birthday did not exceed 45 years. 



4 AGES OF VOLUNTEERS. 

and it is a source of regret that the proper limits of the present 
investigation forbid its extension into the tempting fields of in- 
quiry which their comparison suggests. 

The fact which first attracts attention among the results of this 
research is the marked diversity between the distribution of the 
ages of officers and that of the enlisted men. Each follows a 
clearly manifest law ; in each case the law is deducible with close 
approximation to the truth ; so also is the law governing the ages 
of our population ; yet each of the three is utterly different from 
the other two. The sources of the diversity may well be made 
the object of careful research, and not without a reasonable prob- 
ability of useful results. Certain discordances between the re- 
corded and the computed numbers for a few particular ages will 
be considered hereafter. 

2. Ages of the Unlisted Men. 

The grand total of the rank and file of the volunteers whose 
ages are included in this discussion is shown in the following 
tabular view, which exhibits the recorded age at last birthday for 
the entire number ; although, as already stated, those under 18 
or over 45 (last birthday), 15 626 in all, have been excluded 
from the general discussion. These excluded cases represent two 
classes, viz. the boys, chiefly drummers, musicians, &c, and the 
men who, although past the legal age, were so sturdy or earnest 
that the enrolling officers did not, at that time of great national 
peril, feel justified in insisting on an absolute compliance with 
the legal qualifications. 

In the column entitled " Miscellaneous " are included all those 
organizations which do not belong strictly within the three prin- 
cipal arms of the military service, such as Engineers, Sharpshoot- 
ers, Mounted Infantry, Coast Guards, Marine Brigades, &c, to- 
gether with a few regiments or battalions for which the statistics 
were received after the special computations for Infantry, Cavalry, 
and Artillery had been completed, so that their incorporation with 
these would have required a repetition of the calculations without 
producing any essential change in the result. 



AGES OF VOLUNTEERS. 



TABLE I. 

Classified Summary of Enlisted Volunteers. 



Age 

at last 

birthday. 


ACTUAL NUMBER OF MEN. 


Total 

at each year 

of age. 


Infantry. 


Cavalry. 


Artillery. 


Miscellaneous. 


13 


113 


5 





9 


127 


14 


288 


15 


2 


25 


330 


15 


636 


49 


21 


67 


773 


16 


2053 


232 


61. 


412 


2758 


17 


4653 


638 


226 


908 


6425 


18 


103420 


15013 


5400 


9642 


133475 


19 


71226 


9767 


3439 


5783 


90215 


20 


56238 


7864 


2627 


4329 


71058 


21 


75978 


12081 


4416 


4661 


97136 


22 


57485 


9096 


3107 


3703 


73391 


23 


48954 


7806 


2759 


3198 


62717 


24 


40852 


6361 


2163 


2719 


52095 


25 


36383 


5724 


2012 


2507 


46626 


26 


31292 


4831 


1768 


2352 


40243 


27 


26369 


4192 


1505 


2220 


34286 


28 


27196 


4318 


1525 


2273 


35312 


29 


18833 


2845 


10S7 


1748 


24513 


30 


21937 


3251 


1213 


1959 


28360 


31 


12814 


2053 


796 


2301 


17954 


32 


17038 


2450 


931 


1548 


21967 


33 


13678 


1950 


753 


1598 


17979 


34 


12004 


*1679 


724 


1333 


15740 


35 


14558 


2130 


836 


1456 


18980 


36 


10437 


1541 


702 


1377 


14057 


37 


8782 


1268 


477 


1293 


11820 


38 


10025 


1416 


579 


1326 


13346 


39 


7200 


979 


416 


1001 


9596 


40 


10886 


1441 


649 


1019 


13995 


41 


5634 


822 


320 


659 


7435 


42 


8369 


1199 


535 


826 


10929 


43 


7900 


1079 


533 


828 


10340 


44 


12274 


1851 


796 


1149 


16070 


45 


5509 


954 


289 


260 


7012 


46 


737 


105 


45 


80 


967 


47 


541 


74 


34 


63 


712 


4S 


532 


73 


31 


63 


699 


49 


354 


60 


17 


38 


469 


50 & 


1942 


203 


68 


153 


2366 


over. 










. 



b AGES OF VOLUNTEERS. 

The relative excess of the numbers at certain particular ages, 
and the corresponding defect at others, strikes the attention at 
the first glance. To the former class belong the ages, 21 years, 
most years divisible by 5 (excepting 20 and 45), and those divisi- 
ble by 2 ; to the latter class belong most of those years of age 
whose last digit is 1 or 9. By determining the general law of 
distribution, we may obtain the measure of this excess, and thus 
throw light upon the origin of these discordances. 

The following facts are also manifest, or readily deducible : — 

Of the whole number, 1 012 273, about 1 per centum (.0102), 
were below, and a little more than one half as many (.0052) were 
above, the limits of military age, interpreted as between the ages 
18 and 46. 

Of the number 996 647, within these limits, — 
The average age at last birthday is ... 25.3250 

The average age at time of enlistment is . . . 25.8083 
The age above and below which the numbers are equal is 23.477 
There were of the age 18 years . . . .13.27 per cent, 
under 21 years .... 29.52 " 
under 25 years . . . .58.34 " 
under 30 years .... 76.57 " 

The very close accordance of the proportional numbers for the 
total face of about a million of men from all the loyal States, with 
those deduced * by Mr. Elliott for less than 51 000 men from the 
single State of Massachusetts, is very striking. Tables for the 
individual States and groups of States, herewith presented, unite 
in corroborating the inference that this distribution is due to no 
special local influences, but to a general and overruling law, which 
varies but slightly through widely distant regions of our country, 
and seems scarcely affected by any influences dependent upon 
immigration from abroad. 

This law, which was found by Mr. Elliott to hold good also for 
the Massachusetts troops, shows the number of volunteers (en- 
listed men, not including officers) at each successive year of age 
to form a series of which the first differences are in geometrical 
progression. 

• When the ratio of this geometrical progression is unity, the 

* " On the Military Statistics of the United States of America," Proceedings of the 
International Statistical Congress, V Session, 1S63, p. 32. 



AGES OF VOLUNTEERS. 7 

progression becomes arithmetical ; when, as in the present case, 
it is less than unity, we have a decreasing rate of change. 

Let this ratio be denoted by h, and the number of men at any 

given year of age be 

Xn = b + c(l-h)h" (1) 

so that the total number at and over that age will be 

s n = a — bn-\-ch n (2) 

in which n denotes the excess of the age above 18 years, at which 

epoch 

s = a -f- c. 

The constants a, b, c, h are to be determined, and we have 

jx Q = c(l— h)% jx n = ch n (l — h)\ j m x mn = ch mn (l — h m y 

whence 

fan _ dmX mn /g\ 

Am. x (m + 1) n 

which enables us to determine h from the most convenient equi- 
distant portions of the series. 

The variation of the fundamental equation (2) gives for any 
change in the values of the constants 

&*„ = aa — n^b + h n & + nch n - 1 M, (4) 

by means of which, after an approximate value of h has been 
deduced from (3), and corresponding values of a, b, c derived 
from the numerical data for any four years, the corrected values 
of all four constants may be derived by the method of least 
squares. 

The total number up to any given age, or the definite sum from 
x to x n , is evidently 

s - s n = bn + c (1 — A") = 5J* (5) 

so that 



or by (2) 



»+s*"=s( c -s: af ) 



= \ (*» - «)• (6) 



Since the numerical values deduced from the tables belong not to 
the age n years, but to that age which corresponds to the average 



8 AGES OF VOLUNTEERS. 

for all the individuals between n and n-\-l years, the constants 
deduced hold good also for the series of these mean ages ; the 
successive annual arguments being really at intervals differing 
slightly from one year. 

The age t corresponding to this average may be deduced for 
any year with sufficient accuracy for all practical purposes, by put- 
ting n — t in the first member of equation (6), and using in the 
last member the value of s n+i instead of s n , which gives 

-< + ^ = ^( Sn+i -a). (7) 

Similarly we may find the age corresponding to the average for 
any period of years. For this purpose we replace s n+i in the last 
member of the equation (7) by 

*(* + *)=« — * *(n + nO + *e(*» + *0 

and the corresponding value of t is the age equivalent to the 
average of the period included between n and ri. 

Proceeding as above described, and, after the first approximate 
determination of h, a, b, c, from four conveniently situated and 
equidistant observed values of s n , obtaining improved values for 
all four constants by the method of least squares, the formulas 
derived from the grand total of all the enlisted men of military 
age as presented in Table I. are these, which express the relative 
numbers for every ten thousand : — 

x n = -f 77.04 + 1156.0 • 0.85362" 

*„ = 2102.8 — 77.04 n + 7897.2 • 0.85362". 

With these values the fourth and seventh columns of Table II. 
are computed, the third and sixth columns showing the "ob- 
served," or recorded numbers, reduced to the same scale ; and 
the fifth and eighth columns exhibiting the discordances between 
the calculated and observed values. 

These discordances, although in one sense regular, inasmuch as 
the larger ones are apparently not the result of so-called accident, 
or, in other words, of the use of numbers insufficient to eliminate 
discordances of no palpable significance, are in another sense 
markedly devoid of regularity, inasmuch as the positive and neg- 
ative signs alternate freely, and no decided indication seems to 
exist of a systematic deviation of the general formula. 



AGES OF VOLUNTEERS. 

TABLE II. 

Grand Total of Enlisted Men. 



Age 

at last 

birthday. 


Number. 


Proportion 
giveL 

Observed. 


at and over 
age. 

Calculated. 


Difference. 
(C. - O.) 


Propc 
at givt 

Observed. 


rtion 
n age. 

Calculated. 


Difference. 
(C. - 0.) 


13 


127 














14 


330 














15 


773 














16 


2758 














17 


6425 














18 


133475 


10000 


10000 





1339 


1233 


-106 


19 


90215 


8661 


8767 


+106 


905 


1064 


+ 159 


20 


71058 


7756 


7703 


- 53 


713 


919 


+206 


21 


97136 


7043 


6784 


-259 


975 


796 


-179 


22 


73391 


6068 


5988 


- 80 


736 


691 


- 45 


23 


62717 


5332 


5297 


- 35 


629 


601 


- 28 


24 


52095 


4703 


4696 


- 7 


523 


524 


+ 1 


25 


46626 


4180 


4172 


- 8 


468 


460 


- 8 


26 


40243 


3712 


3712 





404 


403 


- 1 


27 


34286 


3308 


3309 


+ 1 


344 


355 


+ 11 


28 


35312 


2964 


2954 


- 10 


354 


315 


- 39 


29 


24513 


2610 


2641 


+ 31 


246 


280 


+ 34 


30 


28360 


2364 


2361 


- 3 


285 


250 


- 35 


31 


17954 


2079 


2111 


+ 32 


181 


225 


+ 44 


32 


21967 


1898 


1886 


- 12 


221 


203 


- 18 


33 


17979 


1677 


1683 


+ 6 


181 


185 


+ 4 


34 


15740 


1496 


1498 


+ 2 


158 


169 


+ 11 


35 


1S980 


1338 


1329 


- 9 


191 


156 


- 35 


36 


14057 


1147 


1173 


+ 26 


141 


144 


+ 3 


37 


11820 


1006 


1029 


+ 23 


118 


134 


+ 16 


38 


13346 


888 


895 


+ 7 


133 


126 


- 7 


39 


9596 


755 


769 


+ 14 


96 


118 


+ 22 


40 


13995 


659 


651 


- 8 


141 


112 


- 29 


41 


7435 


518 


539 


+ 21 


74 


107 


+ 33 


42 


10929 


' 444 


432 


- 12 


109 


103 


- 6 


43 


10340 


335 


329 


- 6 


104 


99 


- 5 


44 


16070 


231 


230 


- 1 


161 


96 


- 65 


45 


7012 


70 


134 


+ 64 


70 


93 


+ 23 


46 


967 














47 


712 














4S 


699 














49 


469 














50 & 


2366 












1 


over. 














1 



10 AGES OF VOLUNTEERS. 

The trustworthiness of the equations from which the " calcu- 
lated " numbers in this table are derived will be readily esti- 
mated upon inspection of the two columns which exhibit the 
difference between the calculated and observed numbers at the 
different years of age ; and the substitution of the numerical 
values of the constants in equations (6) and (7) enables us to 
determine without difficulty the actual average age which corre- 
sponds to any given " age last birthday." 

Making these numerical substitutions, the equations assume the 
form 

— n + 102.507 (0.85362)" = — 27.2949 -f 0.01298027 s n (8) 

t — 102.507 (0.85362)' = — 27.2949 -f 0.01298027 s n+i (9) 

and yield at once the true ages corresponding to the average of 
the ages " at last birthday," which will be found as follows : — 



Age last 
birthday. 

18 


Corresponding 
average age. 

18.4814 


23 


23.4826 


28 


28.4843 


33 


33.4885 


38 


38.4924 


43 


43.4956 


45 


45.4968 



Intermediate values may be found by interpolation with all need- 
ful accuracy. 

Tables similar to Table II. prepared for each arm of the services 
independently, and for nine States or groups of States, and num- 
bered as Tables III. to XIY. inclusive, are appended. 

Such tables were originally constructed for a much larger num- 
ber of groups ; but these twelve will abundantly suffice to make 
manifest all the marked phenomena which the more detailed 
series has brought to light. 



AGES OF VOLUNTEERS. 

TABLE III. 

United States Volunteer Infantry. 



11 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion 
epecifi 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion 
of a 

Observed. 


it each year 

ge. 

Calculated. 


Difference. 
(0.-O.) 


13 


113 














14 


288 














15 


636 














16 


2053 














17 


4653 














18 


103420 


10000 


10000 





1337 


1252 


- 85 


19 


71226 


8663 


8748 


+ 85 


921 


1078 


+157 


20 


56238 


7742 


7670 


- 72 


727 


921 


+194 


21 


75978 


7015 


6749 


-266 


983 


802 


-181 


22 


57485 


6032 


5947 


- 85 


743 


69.4 


- 49 


23 


48954 


5289 


5253 


- 36 


633 


602 


- 31 


24 


40852 


4656 


4651 


- 5 


528 


524 


- 4 


25 


36383 


4128 


4127 


- 1 


470 


458 


- 12 


26 


31292 


3658 


3669 


+ 11 


405 


401 


- 4 


27 


26369 


3253 


3268 


+ 15 


341 


353 


+ 12 


28 


27196 


2912 


2915 


+ 3 


352 


312 


- 40 


29 . 


18833 


2560 


2603 


.+ 43 


244 


276 


+ 32 


30 


21937 


2316 


2327 


+ 11 


284 


247 


- 37 


31 


12814 


2032 


2080 


+ 48 


166 


221 


+ 55 


32 


17038 


1866 


1859 


- 7 


220 


200 


- 20 


33 


13678 


1646 


1659 


+ 13 


177 


181 


+ 4 


34 


12004 


1469 


1478 


+ 9 


155 


166 


+ 11 


35 


14558 


1314 


1312 


- 2 


188 


152 


- 36 


36 


10437 


1126 


1160 


+ 34 


135 


141 


+ 6 


37 


8782 


991 


1019 


+ 28 


114 


131 


+ 17 


38 


10025 


877 


888 


+ 11 


130 


123 


- 7 


39 


7200 


747 


765 


+ 18 


93 


116 


+ 23 


40 


10886 


654 


649 


- 5 


141 


110 


- 31 


41 


5634 


513 


539 


+ 26 


73 


105 


+ 32 


42 


8369 


440 


434 


- 6 


108 


101 


- 7 


43 


7900 


332 


333 


+ 1 


102 


97 


- 5 


44 


12274 


230 


236 


+ 6 


159 


94 


- 65 


45 


5509 


71 


142 


+ 71 


71 


91 


+ 20 


46 


737 














47 


541 














48 


532 














49 


354 














50 


1942 












1 



12 



AGES OF VOLUNTEERS. 

TABLE IV. 

United States Volunteer Cavalry. 



Age 
1 at last 
birthday. 


Number. 

at each year 

of age. 


Proportion 
specifi 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion t 
of a 

Observed. 


it each year 
Calculated. 


Difference. 
(C. - O.) 


13 


5 














1 U 


15 














15 


49 














16 


232 














17 


638 














18 


15013 


10000 


10000 





1295 


1240 


- 55 


19 


9767 


8705 


8760 


+ 55 


842 


1074 


+232 


20 


7864 


7863 


7686 


-177 


682 


931 


+249 


21 


12081 


7181 


6755 


-426 


1042 


808 


-234 


22 


90.96 


6139 


5947 


-192 


784 


703 


- 81 


23 


7806 


5355 


5244 


-111 


673 


612 


- 61 


24 


6361 


4682 


4632 


- 50 


549 


534 


- 15 


25 


5724 


4133 


4098 


- 35 


494 


467 


- 27 


1 26 


4831 


3639 


3631 


- 8 


417 


410 


- 7 


27 


4192 


3222 


3221 


- 1 


360 


360 





28 


4318 


2862 


2861 


- 1 


372 


318 


- 54 


29 


2845 


2490 


2543 


+ 53 


245 


281 


+ v 36 


30 


3251 


2245 


2262 


+ 17 


280 


250 


- 30 


31 


2043 


1965 


2012 


+ 47 


176 


223 


+ 47 


32 


2450 


1789 


1789 





211 


200 


- 11 


1 33 


1950 


1578 


1589 


+ 11 


168 


180 


+ 12 


34 


1679 


1410 


1410 





145 


163 


+ 18 


' 35 


2130 


1265 


1247 


- 18 


184 


148 


- 36 


! 36 


1541 


10S1 


1098 


+ 17 


133 


135 


+ 2 


37 


1268 


948 


963 


+ 15 


109 


124 


+ 15 


38 


1416 


839 


839 





122 


115 


- 7 


| 39 


979 


717 


724 


+ 7 


84 


107 


+ 23 


40 


1441 


633 


618 


- 15 


124 


100 


- 24 


41 


822 


509 


518 


+ 8 


71 


94 


+ 23 


42 


1199 


438 


426 


- 12 


103 


89 


- 14 


43 


1079 


335 


337 


+ 2 


93 


85 


- 8 


44 


1851 


242 


252 


+ 10 


160 


81 


-79 


45 


954 


82 


170 


+ 88 


82 


78 


- 4 


46 


105 














47 


74 














! 48 


73 














i 49 


60 














50 

1 


203 















AGES OF VOLUNTEERS. 

TABLE V . 

United States Volunteer Artillery. 



13 



Age 

at last 

birthday. 


Number 

at eacb. year 

of age. 


Proportion 
specifi 

Observed. 


at and over 
;d age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion i 
of a 

Observed. 


it each year 
ge. 

Calculated. 


Difference. 
(C.-O.) 


14 


2 














15 


21 














16 


61 














17 


226 














18 


5400 


10000 


10000 





1275 


1179 


- 96 


19 


3439 


8725 


8821 


+ 96 


812 


1024 


4212 


20 


2627 


7913 


7797 


-116 


620 


891 


+271 


21 


4416 


7293 


6906 


-387 


1042 


776 


-266 


22 


3107 


6251 


6130 


-121 


• 734 


678 


- 56 


23 


2759 


5517 


5452 


- 65 


651 


593 


- 58 


24 


2163 


4866 


4859 


- 7 


511 


521 


+ 10 


25 


2012 


4355 


4338 


- 17 


475 


459 


- 16 


26 


1768 


3880 


3879 


- 1 


417 


405 


- 12 


27 


1505 


3463 


3474 


+ 11 


355 


359 


+ 4 


28 


1525 


3108 


3115 


+ 7 


360 


320 


- 40 


29 


1087 


2748 


2795 


+ 47 


257 


286 


+ 29 


30 


1213 


2491 


2509 


+ 18 


286 


257 


- 29 


31 


796 


2205 


2252 


+ 47 


188 


232 


+ 44 


32 


931 


2017 


2020 


+ 3 


220 


211 


- 9 


33 


753 


1797 


1809 


+ 12 


178 


193 


+ 15 


34 


724 


1619 


1616 


- 3 


171 


177 


+ 6 


35 


836 


1448 


1439 


- 9 


197 


163 


- 34 


36 


702 


1251 


1276 


+ 25 


166 


151 


- 15 


37 


477 


1085 


1125 


+ 40 


113 


142 


+ 29 


38 


579 


972 


983 


+ 11 


137 


133 


- 4 


39 


416 


835 


850 


+ 15 


98 


126 


+ 28 


40 


649 


737 


724 


- 13 


153 


119 


- 34 


41 


320 


584 


605 


+ 21 


76 


114 


+ 38 


42 


535 


508 


491 


- 17 


126 


109 


- 17 


43 


533 


382 


382 





126 


105 


- 21 


44 


796 


256 


277 


+ 21 


188 


102 


- 86 


45 


289 


68 


175 


+107 


68 


100 


+ 32 


46 


45 














47 


34 














48 


31 














49 


17 














50 


68 















14 AGES OF VOLUNTEERS. 

TABLE VI. 

Ages of Maine, New Hampshire, Vermont, and Connecticut VoVs. 



Age 

at last 

birthday. 


Number. 

at each year 

of age. 


Proportion 
specifi 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion 
of a 

Observed. 


it each year 
Calculated. 


Difference. 
(C. - O.) 


13 


3 














14 


10 














15 


27 














16 


95 














17 


223 














18 


11694 


10000 


10001 


+ 1 


1522 


1245 


-277 


19 


6541 


8478 


8756 


+278 


852 


1071 


4219 


20 


5311 


7626 


7685 


+ 59 


691 


923 


+232 


21 


7477 


6935 


6762 


-173 


976 


800 


-176 


22 


5356 


5959 


5962 


+ 3 


699 


685 


- 14 


23 


4614 


5260 


5277 


+ 17 


604 


598 


- 6 


24 


3824 


4656 


4679 


+ 23 


500 


519 


+ 19 


25 


3357 


4156 


4160 


+ 4 


440 


453 


+ 13 


26 


2988 


3716 


3707 


- 9 


390 


397 


+ 7 


27 


2590 


3326 


3310 


- 16 


338 


350 


+ 12 


28 


2762 


2988 


2960 


- 28 


361 


307 


- 54 


29 


1881 


2627 


2653 


+ 26 


245 


273 


+ 28 


30 


1983 


2382 


2380 


- 2 


259 


243 


- 16 


31 


1362 


2123 


2137 


+ 14 


177 


218 


+ 41 


32 


1609 


1946 


1919 


- 27 


210 


196 


- 14 


33 


1427 


1736 


1723 


- 13 


185 


178 


- 7 


34 


1141 


1551 


1545 


- 6 


149 


163 


+ 14 


35 


1355 


1402 


1382 


- 20 


176 


149 


- 27 


36 


1046 


1226 


1233 


+ 7 


136 


138 


+ 2 


37 


989 


1090 


1095 


+ 5 


127 


' 128 


+ 1 


38 


1005 


963 


967 


+ 4 


131 


118 


- 13 


39 


817 


832 


849 


+ 17 


107 


115 


+ 8 


40 


969 


725 


734 


+ 9 


127 


108 


- 19 


41 


604 


598 


626 


+ 28 


77 


102 


+ 25 


42 


882 


521 


524 


+ 3 


115 


97 


- 18 


43 


870 


406 


427 


+ 21 


113 


95 


- 18 


44 


1789 


293 


332 


+ 39 


233 


90 


-143 


45 


459 


60 


242 


+182 


60 


88 


+ 28 


46 


50 














47 


38 














48 


34 














49 


23 














50 & 


60 














over. 

















AGES OF VOLUNTEERS. 

TABLE VII. 

Ages of Massachusetts Volunteers. 



15 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion 
specifi 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion 
of a 

Observed. 


it each year 
ge. 

Calculated. 


Difference. 
(C.-O.) 


12 


4 














13 


4 














14 


26 














15 


44 














16 


101 














17 


289 














18 


6894 


10000 


10000 





1269 


1145 


-124 . 


19 


4582 


8731 


8855 


+124 


846 


1002 


+156 


20 


3604 


7885 


7853 


- 32 


666 


877 


+211 


21 


5429 


7219 


6976 


-243 


1003 


771 


-232 


22 


3860 


6216 


6205 


- 11 


713 


678 


- 35 


23 


3203 


5513 


5527 


+ 14 


592 


597 


+ 5 


24 


2871 


4921 


4930 


+ 9 


530 


528 


- 2 


25 


2474 


4391 


4402 


+ 11 


457 


467 


+ 10 


26 


2232 


3934 


3935 


+ 1 


412 


415 


+ 3 


27 


1962 


3522 


3520 


- 2 


362 


370 


+ 8 


28 


2041 


3160 


3150 


- 10 


377 


330 


- 47 


29 


1411 


2783 


2820 


+ 37 


260 


296 


+ 36 


30 


1564 


2523 


2524 


+ 1 


288 


267 


- 21 


31 


988 


2235 


2257 


+ 22 


183 


242 


+ 59 


32 


1233 


2042 


2015 


- 27 


228 


219 


- 9 


33 


1041 


1814 


1796 


- 18 


193 


200 


+ 7 


34 


980 


1621 


1596 


- 25 


181 


184 


+ 3 


35 


1213 


1440 


1412 


- 28 


224 


169 


- 55 


36 


761 


1216 


1243 


+ 27 


141 


157 


+ 16 


37 


699 


1075 


1086 


+ 11 


129 


146 


+ 17 


38 


828 


946 


940 


- 6 


153 


137 


- 16 


39 


600 


793 


803 


+ 10 


111 


129 


+ 18 


40 


838 


682 


674 


- 8 


155 


122 


- 33 


41 


440 


527 


552 


+ 25 


81 


116 


+ 35 


42 


658 


446 


436 


- 10 


122 


110 


- 12 


43 


596 


324 


326 


+ 2 


110 


106 


- 4 


44 


859 


214 


220 


+ 6 


159 


102 


- 57 


45 


296 


55 


118 


+ 63 


55 


98 


+ 43 


46 


28 














47 


14 














48 


16 














49 


9 














50 & 


33 














over. 

















16 



AGES OF VOLUNTEERS. 

TABLE VIII. 

Ages of New York Volunteers. 



J 

Age 

at last 

birthday. 


Number. 

at each year 

of age. 


Proportion 
specifi 

Observed. 


it and over 
3d age. 

Calculated. 


Difference. 
(C.-O.) 


Proportion a 
of a{ 

Observed. 


t each year 
Calculated. 


Difference. 
(C.-O.) 


13 


17 








• 






14 


63 














15 


153 














16 


448 














17 


699 














. 18 


19737 


10000 


10000 





1087 


1173 


+ 86 


19 


16233 


8913 


8827 


- 86 


894 


1019 


+125 


20 


11286 


8019 


7808 


-211 


621 


887 


+266 


21 


20227 


7398 


6922 


-476 


1114 


773 


-341 


22 


13689 


6284 


6149 


-135 


754 


675 


- 79 


23 


11516 


5530 


5774 


+244 


634 


592 


- 42 


24 


9488 


4896 


4882 


- 14 


523 


520 


- 3 


25 


8648 


4373 


4363 


- 10 


476 


459 


- 17 


26 


7285 


3897 


3904 


+ 7 


401 


406 


+ 5 


27 


6223 


3496 


3498 


+ 2 


343 


360 


+ 17 


28 


6652 


3153 


3138 


- 15 


366 


322 


- 44 


29 


4552 


2787 


2816 


+ 29 


251 


289 


+ 38 


30 


5474 


2536 


2527 


- 9 


301 


260 


- 41 


31 


3287 


2235 


2267 


+ 32 


181 


236 


+ 55 


32, 


4533 


2054 


2031 


- 23 


249 


215 


- 34 


33 


3330 


1805 


1816 


+ 11 


184 


197 


+ 13 


34 


3135 


1621 


1619 


- 2 


173 


182 


+ 9 


35 


3885 


1448 


1437 


- 11 


114 


168 


+ 54 


36 


2S72 


1234 


1269 


+ 35 


158 


157 


- 1 


37 


2201 


1076 


1112 


+ 36 


121 


146 


+ 25 


38 


2709 


955 


966 


+ 11 


149 


139 


- 10 


39 


1858 


806 


827 


+ 21 


103 


132 


+ 29 


40 


3157 


703 


695 


- 8 


173 


126 


- 47 


41 


1268 


530 


569 


+ 39 


70 


121 


+ 51 


42 


2302 


460 


448 


- 12 


127 


116 


- 11 


43 


2068 


333 


332 


- 1 


114 


112 


- 2 


44 


3148 


219 


220 


+ 1 


173 


109 


- 64 


45 


831 


46 


111 


+ 65 


46 


106 


+ 60 


46 


87 














47 


41 














48 


53 














49 


23 














50 & 


103 














over. 












* — 





AGES OF VOLUNTEERS. 

TABLE IX. 

Ages of Pennsylvania Volunteers (including Reserves). 



17 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion 
specifi 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion at each year 
of age. 

Observed. Calculated. 


Difference. 
(C.-O.) 


13 


23 




• 










14 


51 














15 


85 














16 


241 














17 


486 














18 


13052 


10000 


10000 





1137 


1339 


+202 


19 


11410 


8863 


8661 


-202 


994 


1131 


+ 137 


20 


8234 


7869 


7530 


-339 


717 


959 


+242 


21 


13336 


7152 


6571 


-581 


1161 


814 


-347 


22 


9376 


5991 


5757 


-234 


816 


694 


-122 


23 


7696 


5175 


5063 


-112 


670 


595 


- 75 


24 


6061 


4505 


4468 


- 37 


528 


510 


- 18 


25 


5375 


3977 


3958 


- 19 


468 


441 


- 27 


26 


4420 


3509 


3517 


+ 8 


385 


382 


- 3 


27 


3576 


3124 


3135 


+ 11 


311 


334 


+ 23 


28 


3817 


2813 


2801 


- 12 


332 


293 


- 39 


29 


2644 


2481 


2508 


+ 27 


230 


260 


+ 30 


30 


2926 


2251 


2248 


- 3 


255 


232 


- 23 


31 


2029 


1996 


2016 


+ 20 


177 


208 


+ 31 


32 


2375 


1819 


1808 


- 11 


207 


188 


- 19 


33 


1903 


1612 


1620 


+ 8 


166 


173 


+ 7 


34 


1657 


1446 


1447 


+ 1 


144 


158 


+ 14 


35 


2089 


1302 


1289 


- 13 


182 


147 


- 35 


36 


1490 


1120 


1142 


+ 22 


13« 


138 


+ 8 


37 


1290 


990 


1004 


+ 14 


112 


130 


+ 18 


38 


1434 


878 


874 


- 4 


125 


124 


- 1 


39 


1141 


753 


750 


- 3 


99 


118 


+ 19 


40 


1692 


654 


632 


- 22 


147 


113 


- 34 


41 


918 


507 


519 


+ 12 


80 


109 


+ 29 


42 


1431 


427 


410 


+ 17 


124 


106 


- 18 


43 


1318 


303 


307 


+ 4 


115 


103 


- 12 


44 


1674 


188 


206 


+ IS 


146 


101 


- 45 


45 


480 


42 


105 


+ 63 


42 


99 


+ 57 


46 


73 














47 


46 














48 


49 














49 


36 














50 & 


109 














over. 














■ — ' 



18 



AGES OF VOLUNTEERS. 

TABLE X. 

Ages of Ohio Volunteers. 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion 
specif! 

Observed. 


it and over 
jd age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion a 
of ag 

Observed. 


t each year 
re- 
calculated. 


Difference. 
(C. - O.) 


13 


21 




* 










14 


44 














15 


103 














16 


470 














17 


1476 














18 


23495 


10000 


10000 





1567 


1359 


-208 


19 


14986 


8433 


8641 


+208 


999 


1143 


+144 


20 


12358 


7434 


7498 


+ 64 


825 


963 


+ 138 


21 


12819 


6609 


6535 


- 74 


855 


815 


- 40 


22 


10499 


5754 


5720 


- 34 


700 


692 


- 8 


23 


9297 


5054 


5028 


- 26 


620 


590 


- 30 


24 


7327 


4434 


4438 


- 6 


489 


505 


+ 16 


25 


6502 


3945 


3933 


- 12 


430 


435 


+ 5 


26 


5678 


3515 


3498 


- 17 


382 


377 


- 5 


27 


4739 


3133 


3121 


- 12 


316 


329 


+ 13 


28 


4997 


2817 


2792 


- 25 


333 


289 


- 44 


29 


3570 


2484 


2503 


+ 19 


238 


256 


+ 18 


30 


3960 


2246 


2247 


+ 1 


264 


228 


- 36 


31 


2596 


1982 


2019 


+ 37 


174 


206 


+ 32 


32 


3029 


1808 


1813 


+ 5 


201 


187 


- 14 


33 


2669 


1607 


1626 


+ 19 


178 


171 


- 7 


34 


2302 


1429 


1455 


+ 26 


154 


159 


+ 5 


35 


2659 


1275 


1296 


+ 21 


178 


148 


- 30 


36 


2216 


• 1097 


1148 


+ 51 


147 


139 


- 8 


37 


1830 


950 


1009 


+ 59 


123 


132 


+ 9 


38 


1959 


827 


877 


+ 50. 


130 


125 


- 5 


39 


1424 


697 


752 


+ 55 


95 


120 


+ 25 


40 


1880 


602 


632 


+ 30 


126 


116 


- 10 


41 


1097 


476 


516 


+ 40 


73 


113 


+ 40 


42 


1513 


403 


403 





101 


110 


+ 9 


43 


1337 


302 


293 


- 9 


89 


108 


+ 19 


44 


2070 


213 


185 


- 28 


138 


106 


- 32 


45 


1128 


75 


79 


+ 4 


75 


104 


+ 29 


46 


202 














47 


161 














48 


145 














49 


104 














50 & 


471 














over. 














1 



AGES OF VOLUNTEERS. 

TABLE XI. 

Ages of Indiana Volunteers. 



19 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion 
speciti 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion < 
of a 

Observed. 


it each year 
Be- 

Calculated. 


1 
Difference. 

(C.-O.) 


13 


13 














14 


16 














15 


39 














16 


162 














17 


578 














18 


11178 


10000 


10000 





1608 


1446 


-162 


19 


7175 


8392 


8554 


+162 


1032 


1223 


+191 


20 


6478 


7360 


7331 


- 29 


932 


1035 


+103 


21 


6398 


6428 


6296 


-132 


920 


877 


- 43 


22 


5580 


5508 


5419 


- 89 


802 


744 


- 58 


23 


4562 


4706 


4675 


- 31 


656 


632 


-24 


24 


3782 


4050 


4043 


- 7 


544 


538 


- 6 


25 


3216 


3506 


3505 


- 1 


462 


460 


- 2 


26 


2707 


3044 


3045 


+ 1 


390 


394 


+ 4 


27 


2269 


2654 


2651 


- 3 


326 


337 


+ 11 


28 


2272 


2328 


2314 


- 14 


327 


290 


- 37 


29 


1513 


2001 


2024 


+ 23 


217 


251 


+ 34 


30 


1799 


1784 


1773 


- 11 


259 


218 


- 41 


31 


1013 


1525 


1555 


+ 30 


145 


190 


+ 45 


32 


1230 


1380 


1365 


- 15 


177 


166 


- 11 


33 


1046 


1203 


1200 


- 3 


151 


146 


- 5 


34 


871 


1052 


1053 


+ 1 


125 


130 


+ 5 


35 


962 


927 


923 


- 4 


138 


116 


- 22 


36 


666 


789 


806 


+ 17 


96 


104 


+ 8 


37 


589 


693 


702 


+ 9 


85 


94 


+ 9 


38 


656 


608 


608 





94 


86 


- 8 


39 


428 


514 


522 


+ 8 


62 


79 


+ 17 


40 


683 


452 


443 


- 9 


98 


73 


- 25 


41 


371 


354 


370 


+ 16 


53 


68 


+ 15 


42 


482 


301 


302 


+ 1 


69 


64 


- 5 


43 


471 


232 


238 


+ 6 


68 


60 


- 8 


44 


682 


164 


178 


+ 14 


98 


57 


- 41 


45 


457 


66 


121 


+ 55 


66 


55 


- 11 


46 


70 














47 


37 














48 


50 














49 


24 














50 & 


146 














over. 














I 



20 



AGES OF VOLUNTEERS. 

TABLE XII. 

Ages of Michigan Volunteers. 



Age 

at last 

birthday. 


Number. 

at each year 

of age. 


Proportion 
specifi 

Observed. 


it and over 
3d age. 

Calculated. 


Difference. 
(C.-O.) 


Proportion a 

of a 

Observed. 


t each year 
Calculated. 


Difference. 
(C. - O.) 


13 


3 














14 


9 














15 


27 














16 


112 














17 


299 














18 


5862 


10000 


10000 





1523 


1279 


-244 


19 


3437 


8477 


8721 


+244 


893 


1098 


+205 


20 


2767 


7584 


7623 


+ 39 


719 


943 


+224 


21 


3727 


6865 


6680 


-185 


968 


812 


-156 


22 


2802 


5897 


5868 


- 29 


728 


700 


- 28 


23 


2337 


5169 


5168 


- 1 


607 


605 


- 2 


24 


1963 


4562 


4563 


+ 1 


510 


524 


+ 14 


25 


1724 


4052 


4039 


- 13 


448 


455 


+ 7 


26 


1568 


3604 


3584 


- 20 


407 


396 


- 11 


27 


1297 


3197 


3188 


- 9 


337 


346 


+ 9 


28 


1335 


2860 


2842 


- 18 


347 


304 


- 43 


29 


923 


2513 


2538 


+ 25 


240 


268 


+ 28 


30 


989 


2273 


2270 


- 3 


257 


237 


- 20 


31 


695 


2016 


2033 


+ 17 


180 


211 


+ 31 


32 


843 


1836 


1822 


- 14 


219 


188 


- 31 


33 


614 


1617 


1634 


+ 17 


160 


169 


+ 9 


34 


527 


1457 


1465 


+ 8 


137 


153 


+ 16 


35 


668 


1320 


1312 


- 8 


173 


140 


- 33 


36 


481 


1147 


1172 


+ 25 


125 


128 


+ 3 


37 


411 


1022 


1044 


+ 22 


107 


118 


+ 11 


38 


458 


915 


926 


+ 11 


119 


109 


- 10 


39 


313 


796 


817 


+ 21 


81 


102 


+ 21 


40 


466 


715 


715 


+ 


121 


96 


- 25 


41 


256 


594 


619 


+ 25 


67 


91 


+ 24 


42 


403 


527 


528 


+ 1 


105 


86 


- 19 


43 


400 


422 


442 


+ 20 


104 


83 


- 21 


44 


825 


318 


359 


+ 41 


214 


79 


-135 


45 


398 


104 


280 


+176 


104 


77 


- 27 


46 


44 














47 


23 














48 


26 














49 


14 














50 & 


61 














over. 

















AGES OF VOLUNTEERS. 

TABLE XIII. 

Ages of Illinois Volunteers. 



21 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion 
specifi 

Observed. 


at and over 
ed age. 

Calculated. 


Difference. 
(C. - O.) 


Proportion i 

of a 

Observed. 


it each year 
Calculated. 


Difference. 
(C.-O.) 


13 


5 














14 


23 














15 


65 














16 


250 














17 


539 














18 


10167 


10000 


10080 


+ 80 


1070 


942 


-128 


19 


8348 


8930 


9138 


+208 


879 


1043 


+164 


20 


7076 


8051 


8095 


+ 44 


745 


958 


+213 


21 


8709 


7306 


7137 


-169 


916 


858 


- 58 


22 


7441 


6390 


6279 


-111 


783 


766 


- 17 


23 


6872 


5607 


5513 


- 94 


723 


677 


- 46 


24 


6019 


4884 


4836 


- 48 


634 


600 


- 34 


25 


5315 


4250 


4236 


- 14 


559 


529 


- 30 


26 


4441 


3691 


3707 


+ 16 


468 


465 


- 3 


27 


3810 


3223 


3242 


+ 19 


401 


410 


+ 9 


28 


3677 


2822 


2832 


+ 10 


387 


358 


- 29 


29 


2622 


2435 


2474 


+ 39 


276 


315 


+ 39 


30 


2869 


2159 


2159 





302 


276 


- 26 


31 


1847 


1857 


1883 


+ 26 


194 


242 


+ 48 


32 


2076 


1663 


1641 


- 22 


219 


211 


- 8 


33 


1666 


1444 


1430 


- 14 


175 


185 


+ 10 


34 


1508 


1269 


1245 


- 24 


159 


162 


+ 3 


35 


1568 


1110 


1083 


- 27 


165 


142 


- 23 


36 


1243 


945 


941 


- 4 


131 


124 


- 7 


37 


944 


814 


817 


+ 3 


99 


110 


+ 11 


38 


1056 


715 


707 


- 8 


111 


96 


- 15 


39 


725 


604 


611 


+ 7 


77 


87 


+ 10 


40 


1040 


527 


524 


- 3 


109 


77 


- 32 


41 


607 


418 


447 


+ 29 


64 


69 


+ 5 


42 


816 


354 


378 


+ 24 


86 


64 


- 18 


43 


734 


268 


314 


+ 46 


77 


59 


- 18 


44 


1075 


191 


255 


+ 69 


113 


54 


- 59 


45 


737 


78 


201 


+123 


78 


50 


- 28 


46 


88 














47 


86 














48 


78 














49 


45 














50 & 


237 














over. 

















22 



AGES OF VOLUNTEERS. 

TABLE XIV. 

Ages of Wisconsin and Iowa Volunteers. 



Age 

at last 

birthday. 


Number 

at each year 

of age. 


Proportion at and over 
specified age. 

Observed. Calculated. 


Difference. 
(C.-0.) 


Proportion at each year 
of age. 

Observed. Calculated. 


Difference. 
(C.-O.) 


13 


11 














14 


22 














15 


79 














16 


369 














17 


829 














18 


11083 


10000 


10000 





1485 


1221 


-264 


19 


6440 


8515 


8779 


+264 


863 


1048 


+185 


20 


4874 


7652 


7731 


+ 79 


653 


902 


+249 


21 


7082 


6999 


6829 


-170 


949 


778 


-171 


22 


5271 


6050 


6050 





707 


673 


- 34 


23 


4240 


5343 


5377 


+ 34 


569 


585 


+ 16 


24 


3718 


4774 


4792 


+ 18 


499 


510 


+ 11 


25 


3260 


4275 


4282 


+ 7 


437 


447 


+ 10 


26 


2953 


3838 


3835 


- 3 


396 


893 


- 3 


27 


2675 


3442 


3442 





359 


345 


- 14 


28 


2495 


3083 


3097 


+ 14 


334 


310 


- 24 


29 


1844 


2749 


2787 


+ 38 


247 


277 


+ 30 


30 


1973 


2502 


2510 


+ 8 


264 


250 


- 14 


31 


1472 


2238 


2260 


+ 22 


196 


227 


+ 31 


32 


1674 


2042 


2033 


- 9 


224 


207 


- 17 


33 


1432 


1818 


1826 


+ 8 


192 


191 


- 1 


34 


1237 


1626 


1635 


+ 9 


166 


177 


+ 11 


35 


1359 


1460 


1458 


- 2 


182 


165 


- 17 


36 


1154 


1278 


1293 


+ 15 


155 


155 





37 


1022 


1123 


1138 


+ 15 


137 


146 


+ 9 


38 


1104 


986 


992 


+ 6 


148 


139 


- 9 


39 


873 


838 


853 


+ 15 


117 


133 


+ 16 


40 


967 


721 


720 


- 1 


130 


128 


- 2 


41 


670 


591 


592 


+ 1 


90 


124 


+ 34 


42 


886 


501 


468 


- 33 


119 


120 


+ 1 


43 


950 


382 


348 


- 34 


127 


117 


- 10 


44 


1374 


255 


231 


- 24 


184 


114 


- 70 


45 


531 


71 


117 


+ 46 


71 


112 


+ 41 


46 


113 














47 


108 














48 


115 














49 


76 














50 & 


632 














over. 










1 







AGES OF VOLUNTEERS. 23 

The agreement of these several special results with those de- 
duced from their aggregate is remarkable. Only in one case, 
that of the Illinois troops, has the simple formula 

s n = a — bn -\- ch n 

failed to give all desired accordance between theory and observa- 
tion ; and throughout the whole series the same peculiarities in 
the residuals are recognizable. In this connection I may add, 
what is in itself very significant, that attempts to deduce a law 
of distribution of age for troops recruited in Missouri, Kentucky, 
Tennessee, and Virginia have proved fruitless, and only small 
success was attainable for the Maryland volunteers. The infer- 
ence is obvious, that the volunteering of troops from these States 
was not subject to the undisturbed influence of any statistical 
law. In the case of Illinois troops, a curious anomaly manifested 
itself in the residuals, namely, a cyclical or periodic term. This 
was found to be represented with sufficient accuracy by adding 
to the formula a term d sin *i/n ■ 68°, in which d = 314. I know 
of no satisfactory interpretation of this expression, but it has been 
used in the preparation of the table for that State. 

In Table XV. is presented a summary of the results deduced 
from the special groups presented in Tables III. to XIV. All 
the constants are reduced to the same scale, and hold good for 
10 000 troops of the ages 18 to 45 at last birthday, inclusive. 
The mean ages, as here given, refer, not to the last birthday, but 
to the actual date of enlistment. 

The values of the constants for these special tables have been 
determined from a smaller number of equations of condition 
than were used for the grand total. In that each year was spe- 
cially used ; in these the results were deduced from eight normal 
places. 



24 



AGES OF VOLUNTEERS. 



TABLE XV. 

Constants deduced for Special Glasses of Volunteers. 





Number of Sol- 
diers 


Mean age at en- 
listment. 










Class. 








a. 


6. 


C. 


h. 




Of all 
ages. 


Of mili- 
tary age. 


For all. 
25.8362 


For 
18 to 45. 

25.8083 










| Total Enlisted Men 


1012273 


996647 


2102.8 


77.04 


7897.2 


0.8536 


Total Infantry 


785120 


773271 


25.7827 


25.7484 


2080.0 


75.84 


7920.0 


0.8514 


Total Cavalry 


117405 


115951 


25.8110 


25.7795 


1595.0 


57.90 


8405.0 


0.8593 


Total Artillery 


42862 


42357 


26.1576 


26.1202 


2239.0 


81.20 


7761.0 


0.8585 


Me., N.H., Vt., Conn. 


76445 


75881 


25.8792 


25.8423 


2112.0 


73.06 


7S89.0 


0.8511 


Massachusetts 


54705 


54137 


26.0561 


26.0943 


2016.0 


76-40 


7984.0 


0.8662 


New York 


183281 


181594 


26.130S 


26.1642 


2390.5 


88.86 


7609.5 


0.8575 


Pennsylvania 


116043 


114844 


25.8227 


25.8331 


2477.4 


90.20 


7523.0 


0.8340 


Ohio 


153133 


149936 


25.4936 


25.3859 


2625.0 


96.08 


7375.0 


0.8287 


Indiana 


70673 


69536 


24.7100 


24.6858 


1175.0 


42.18 


8825.0 


0.8409 


1 Michigan 


39107 


38489 


25.5290 


25.5276 


1827.0 


61.30 


8173.0 


0.8510 


Illinois 


96409 


95003 


25.9369 


25.8935 


2023.0 


70.66 


8057.0 


0.S558 


j Wisconsin and Iowa 


76987 


74613 


26.1571 


25.9991 


2737.0 


100.20 


7263.0 


0.8456 



In considering the residuals, the most striking feature is the 
excess of the recorded numbers at 18 and 21, which latter excess 
is counterbalanced by a deficiency at 20 and to some extent at 19 
also. The explanation of this is readily found in the facts that 
enlistments of youths under 18 are not valid without the formal 
consent of parents, and that 21 is the period at which minority 
ceases. There can be no reasonable doubt that these residuals 
furnish the measure of the number under 18 and under 21, who 
misstated their age to the mustering officer. At the age of 18 
the discordance is less marked than at 21, since the inducements 
to misstate operated near this age in different directions, many of 
those at 18 probably representing themselves as 21 years old, 
while' their number was made good by others who untruly 
declared themselves as having completed their 18th year. 

The excess of the recorded number at 21 averages 1| per cent., 
that deficiency at 20 is about 2 per cent., and at 19 about If per 
cent. The number recorded for 18 years is in excess by 1 per 
cent., although it varies very considerably in the different groups. 

A large excess, representing the number of those who from 
similar motives understated their ages, is also to be seen at the age 



AGES OF VOLUNTEERS. 25 

of 44 in most States, corresponding to an analogous deficiency at 
45. This varies, however, in different States, owing in all proba- 
bility to the different interpretation by the mustering officers of 
that provision of the law which precluded the acceptance of men 
over 45 years old. The average, in the more elaborately calcu- 
lated table for the grand total, places the number at 44 in excess 
of the computed number by two thirds of its whole amount, and 
leaves that at 45 in defect by one fourth part. 

For all other ages than those enumerated, the regular excess or. 
defect of the residuals furnishes apparently the measure of the 
accuracy with which the ages were stated or recorded. It will be 
seen that at those ages which correspond to what are called round 
numbers, such as those divisible by 10, also, though to a less 
extent, at those divisible by 5, and in a still less but yet recog- 
nizable degree, at those divisible by 2, the recorded numbers are 
in excess; while the adjacent numbers, especially those ending in 
1, 9, and 7, are in defect. The natural tendency which every one 
will recognize, and which inclines us to make use of certain more 
habitually employed numbers, rather than to use a minuteness 
repugnant to some persons, furnishes an adequate and, as I believe, 
the true explanation. 

It will be readily noted that where any two of the above-named 
principles conflict, the residual is diminished ; and that where they 
act in combination it is increased. 

Lines showing the computed and the enrolled numbers of 
enlisted men are given on Chart A, and readily manifest these 
facts to the eye. The other data upon this chart are given for 
comparison, and will be referred to hereafter. It will be borne 
in mind that the numbers given do not, by a large amount, repre- 
sent the actual numbers of enlisted volunteers or of volunteer 
officers, nor probably so much as two fifths of the total number 
of our soldiers in the struggle for national existence. They are 
relative quantities, deduced from only those data cited at the com- 
mencement of this paper, and illustrate, not the actual numbers 
for our troops, but the relative distribution of their ages. 

The same results are presented in another form upon Chart B, 
which exhibits, for the enlisted men, the officers, and the white 
male population, the proportion at and over the specified ages and 
under 45 years, for each 10 000 men of military age. 



26 AGES OF VOLUNTEERS. 

Charts C and B show the law by which the ratios of officers 
and enlisted men to the white male population vary with the age. 
All the numbers are reduced to the scale of ten thousand of pop- 
ulation at 18 years, Chart being constructed in reference to 
the whole United States, and Chart D to the Loyal States only. 

3. Ages of Officers. 

The total number of officers of all ages is 37 184, that of those 
between 18 and 46 being 35953. 

On comparing the numbers at the several ages with the formula 

s n = a — bn-\- ch n 

we find at once that for certain ages the value of h would be an 
impossible one ; and that for other years, which would yield possible 
values, these values are so discordant and the residuals to which 
they lead become so large that it is manifest that the curve can be 
represented neither by this nor by any similar law. 
Many trials have led to the empirical formula 

s n = a — bn* -4- c sin n k 8 (A) 

as that which best represents the character of the curve. The 
extremely complicated manner, however, in which the six constants 
of this equation enter into the formula renders the attainment of 
a solution from six equations, by any direct process, a matter of 
great difficulty and inconvenience. Of course the constant a rep- 
resents the value of *„ for n = 0, so that the problem really con- 
sists in the determination of the five quantities b, c, &', k, and 0. 
Graphic representations of the curve, by showing the points at 
which the third term becomes =0, facilitated the approximate 
determination of these constants, and thus equations of condition 
were formed which have led to quite satisfactory values, giving 
an agreement between the formula and the observed numbers 
nearly if not quite as good as that obtained for the enlisted men 
by the formula already described. 

Subsequently, investigations made for the purpose of extending 
this formula to the ages from 46 to 50 showed a deviation for these 
later years. This* deviation seems only to be reconciled by the 
employment of an additional term containing two more constants, 



AGES OF VOLUNTEERS. 27 

and the term thus found proves applicable to all ages above 30, 
essentially diminishing the residuals for all subsequent years. 
The formula then stands for each 10 000 officers 

s„=10 000 — 736rc a75 + 1259 sinrc 0536 x 45°.64+ 100 sin (n— 12)18° 

in which the last term is only to be employed for positive values 
of n — 12, that is, for ages above 30 years. 

The near agreement of this formula with the observations will 
be recognized on Table XVI., which exhibits for each year of age 
from 18 to 50, as well as for those above 50, the actual and the 
proportionate observed number of officers, both at, and at and over, 
the given age, together with the corresponding numbers as deduced 
from the formula, and the discordances between Computation and 
Observation. 

The dissimilarity of the curves thus found for officers and for 
enlisted men is most striking, as will be perceived by reference to 
Charts A and B. The chief discordance for the officers' curve is 
for the age of 18 years, at which, or at 19, the formula seems to 
fail. This is probably due in part to the fact that comparatively 
few officers were commissioned under the age of legal maturity, 
so that the law governing the distribution by age ought not to be 
regarded as applicable below 21 years. 



28 AGES OF VOLUNTEERS. 

TABLE XVI. 

Ages of Officers of United States Volunteers. 



Age 

at last 

birthday. 


Number 

at given 

age. 


Pro] 
Observed. 


aortion at 
age 

Calcu- 
lated. 


given 

Difference. 
(G.-O.) 


Number 
at and over 
given age. 


Propc 
Observed. 


rtion at an 
given age 

Calcu- 
lated. 


d over 

Difference. 
(C.-O.) 


13 


















14 


















15 


1 








37183 








16 


5 








37182 








17 


5 








37177 








18 


178 


48 


-164 


-212 


37172 


10000 


10000 





19 


409 


110 


+233 


4123 


37094 


9952 


10164 


+212 


20 


687 


185 


351 


+166 


36685 


9842 


9931 


+ 89 


21 


1630 


439 


443 


+ 4 


35998 


9657 


9580 


- 77 


22 


1839 


495 


500 


+ 5 


34368 


9218 


9137 


- 81 


23 


2101 


565 


537 


- 28 


32529 


8723 


8637 


- 86 


24 


2234 


601 


557 


- 44 


30428 


8158 


8100 


- 58 


25 


2161 


581 


567 


- 14 


28194 


7557 


7543 


- 14 


26 


2114 


569 


563 


- 6 


26033 


6976 


6976 





27 


1968 


529 


555 


+ 26 


23919 


6407 


6413 


+ 6 


28 


2071 


557 


536 


- 21 


21951 


5878 


5858 


- 20 


29 


1756 


472 


516 


+ 44 


19880 


5321 


5322 


+ 1 


30 


1836 


494 


457 


- 37 


18124 


4849 


4806 


- 43 


31 


1429 


884 


430 


+ 46 


16288 


4355 


4349 


- 6 


32 


1613 


434 


405 


- 29 


14859 


3971 


3919 


- 52 


33 


1422 


383 


381 


- 2 


13246 


3537 


3514 


- 23 


34 


1324 


356 


359 


+ 3 


11824 


3154 


3133 


- 21 


35 


1434 


386 


335 


- 51 


10500 


2798 


2774 


- 24 


36 


1221 


328 


313 


- 15 


9066 


2412 


2439 


+ 27 


37 


1031 


277 


291 


+ 14 


7845 


2084 


2126 


+ 42 


38 


1033 


278 


269 


- 9 


6814 


1807 


1835 


+ 28 


39 


813 


219 


245 


+ 26 


5781 


1529 


1566 


+ 37 


40 


874 


235 


222 


- 13 


4968 


1310 


1321 


+ 11 


41 


557 


149 


197 


+ 48 


4094 


1075 


1099 


+ 24 


42 


656 


176 


171 


- 5 


3537 


926 


902 


- 24 


43 


485 


130 


148 


+ 18 


2881 


750 


731 


- 19 


44 


598 


161 


124 


- 37 


2396 


620 


583 


- 37 


45 


478 


130 


100 


- 30 


1798 


459 


459 





46 


217 


58 


86 


+ 28 


1320 


329 


359 


+ 30 


47 


184 


50 


70 


+ 20 


1103 


271 


273 


+ 2. 


48 


17.5 


47 


58 


+ 11 


919 


221 


203 


- 18 


49 


121 


33 


55 


+ 22 


744 


174 


145 


- 29 


50 & 


523 


141 


90 


- 51 


523 


141 


90 


- 51 


over. 



















AGES OF VOLUNTKKliS. 



29 



The mean age at last birthday for all the officers is . 30.4406 
" " " for those between 18 & 45 29.8338 

and the mean age of the mean at last birthday is . 29.45 
or about 29.94 at the time of their muster into the service. 
Above and below this age the number of officers was equal. 

The annexed Table XVII. exhibits the relative proportions of 
officers to the enlisted men, and of these to the white male popu- 
lation of the whole United States and of the Loyal States respec- 
tively, as given by the census of 1860, taken less than one year 
before the call to arms. 

The caution must here be repeated, that the " proportion of 
enlisted men to the population," as here given, does not at all 
apply to the armies of the nation during the rebellion. It relates 
solely to the number of volunteer troops here considered ; and 
this Table XVII. is presented solely to make manifest the laws 
according to which the ratios of enlisted men to the population, 
and the ratios of officers to men, varied with the age. 



TABLE XVII. 

Relative Proportions 
of Officers, Enlisted Men, and White Male Population, 
for the first million of Volunteers. 



AGE. 


Proportion of 

Officers to 

Enlisted 

Men. 


Proportion 
of Enlisted 
Men to Popu- 
lation of 
U. States. 


Proportion 
of Enlisted 

Men to Pop- 
ulation of 

Loyal States. 


AGE. 


Proportion of 

Officers to 

Enlisted 

Men. 


Proportion 
of Enlisted 
Men to Popu- 
lation of 
U. States. 


Proportion ' 
of Enlisted 

Men to Pop- 
ulation of 

Loyal States. 


18 


0.001 


0.448 


0.570 


32 


0.072 


0.100 


0.128 


19 


0.007 


0.393 


0.502 


33 


0.074 


0.093 


0.119 


20 


0.013 


0.345 


0.442 


34 


0.076 


0.088 


0.112 


21 


0.019 


0.305 


0.391 


35 


0.077 


0.084 


0.105 


22 


0.025 


0.269 


0.363 


36 


0.078 


0.080 


0.100 


23 


0.031 


0.239 


0.308 


37 


0.077 


0.077 


0.096 


24 


0.037 


0.212 


0.275 


38 


0.075 


0.075 


0.093 


25 


0.043 


0.190 


0.246 


39 


0.073 


0.074 


0.090 


26 


0.04S 


0.170 


0.221 


40 


0.068 


0.073 


0.088 


27 


0.054 


0.154 


0.199 


41 


0.062 


0.073 


0.088 


28 


0.969 


0.139 


0.180 


42 


0.057 


0-07-3 


0.087 


29 


0.063 


0.127 


0.164 


43 


0.049 


0.074 


0.087 


30 


0.065 


0.116 


0.150 


44 


0.041 


0.075 


0.088 


31 


0.068 


0.107 


0.138 


45 


0.033 


0.076 


0.089 



30 AGES OF VOLUNTEERS. 

4. Population of the United States and of the Loyal States. 

The great and unexpected dissimilarity between the law of dis- 
tribution of age for officers and for men led, as I have already 
mentioned, to an investigation of the ages of the white male pop- 
ulation, both of the whole United States, and of the Loyal States 
considered by themselves. And, in the absence of any distinct 
criterion, those States which were free from slavery in 1860, to- 
gether with Delaware, Maryland, Kentucky, and Missouri, have 
been classed as Loyal States. The territory of West Virginia, 
eastern Tennessee, &c, is thus excluded, although inhabited by 
a thoroughly loyal population, which contributed about twenty of 
the regiments here computed ; and about ten other regiments, 
included in our data, were raised in States not accounted loyal. 
But all these are offset by the very considerable portion of the 
inhabitants of the four Slave States above named, from which the 
insurgent army was reinforced. 

The only materials available for the inquiry are contained in 
the tables, derived from the official census of the United States 
in 1860. Of course it is the male population alone which has any 
relation to the present research. 

The difficulty of deducing from these meagre details the num- 
ber of males at each year of military age is apparent at the first 
glance. Had the classification between the ages of 20 and 50 
been in six groups of five years each, instead of three groups of 
ten years, the facility and accuracy of the investigation would have 
been incomparably greater. As it is, the only available data are 
contained in the second column of the following tables, XVIII. 
and XIX. These tables give, in column 9, the results of the 
formulas obtained for representing the observed numbers given 
in column 2. The degree of correctness of these formulas may 
be estimated by means of column 4, which shows the excess of 
the calculated number over the number given by the census, in 
decimals of the latter. The accordance for ages above 20 years is 
remarkably good. Beyond 50 years the agreement is not so close 
as between 20 and 50, but is nevertheless quite tolerabll ; but the 
comparison is omitted here as not pertinent to the subject, since 
none of the census-numbers for groups of ages above 50 have 
been employed in the computation. 



AGES OF VOLUNTEERS. 



31 



The other columns require no explanation. It will be remem- 
bered that the numbers of enlisted men and officers here given 
are merely those belonging to the original volunteer regiments at 
the time of their enlistment, excluding all recruits, substitutes, 
drafted men, &c. Also, that the numbers apply only to those 
regiments which had been mustered into the United States ser- 
vice prior to the collection of our data, as shown on page 2. 

TABLE XVIII. 

White Male Population of the United States in 1860. 

Comparison between Computed and Observed Ages. 



Age at last 
birthday. 


White Male 
of the Uni 

Census. 


Population 
ted Stales. 

Computed. 


Difference. 
(C.-O.) 


Enlisted 
Men of first 
volunteers. 


Officers of 
first vol- 
unteers. 


Ratio to White Male 
Population. 

Men. Officers. 


10- 15 


1 578 274 


1 547 730 


-0.0193 










15-20 


1 391 950 


1 422 340 


+0.0245 










18-20 




553 360 




219 200 


587 


0.395 


0.0011 


20-30 


2 465 276 


2 436 770 


-0.0116 


529 809 


18 561 


0.217 


0.0076 


30-40 


1 847 259 


1 847 810 


0.0000 


165 292 


13 156 


0.090 


0.0071 


40-45 




807 860 




63 607 




0.079 




40-50 


1 215 031 


1 216 690 


+0.0014 




4 868 




0.0040 


18 - 45 




5 645 800 




977 968 









TABLE XIX. 

White Male Population of the Loyal States in 1860. 

Comparison between Computed and Observed Ages. 



Age at last 
birthday. 


White Male 
of the L03 

Census. 


Population 
al States. 

Computed. 


Difference. 
(C.-O.) 


Enlisted 
Men of first 
volunteers. 


Officers of 
first vol- 
unteers. 


Ratio to 
Popr. 

Men. 


SVhite Male 

lation. 

Officers. 


10-15 


1 211 521 


1 179 260 


-0.0266 










15-20 


1 095 934 


1 110 770 


+0.0135 










18-20 




435 100 




219 200 


587 


0.502 


0.0014 


20-30 


1 971 486 


1 956 890 


-0.0075 


529 809 


18 561 


0.271 


0.0095 


30-40 


1 517 736 


1 517 720 


0.0000 


165 292 


13 156 


0.109 


0.0087 


40-45 


• 


664 510 




63 667 




0.096 




40 - 50 


996 481 


996 350 


0.0000 




4 868 




0.0049 


18 - 45 




4 574 220 




977 968 









32 AGES OF VOLUNTEERS. 

The formulas which thus represent the number of white males 
from the age of 10 years upwards are, — 

for the United States 

x = 445440 sin (134° 34' -f- (y — 10) • 52') 

for the Loyal States 

x = 257 870 sin (111° 6"'.l -p (y — 10) • 80'.2) 

in which x is the number at the year of age y. 

Assuming these values to be correct, we find the distribution 
of the white male population in 1860 to have been as represented 
in Tables XX. and XXI. 

These tables show, for the United States and the Loyal States 
respectively, the actual numbers : — first, at each year of age 
from 15 to 50, inclusive ; secondly, at and over each year of age 
from 15 to 50, inclusive ; thirdly, at and over each year within 
the limits of military age from 18 upwards, and also the cor- 
responding relative or proportional numbers, using those for 18 
years as the units. 

Subsequent investigation has led to the detection of a formula 
totally different in structure from those above given, but which, 
although its agreement with the census-numbers within the years 
of military age is by no means so close as these afford, yet repre- 
sents the various censuses of the United States and those of for- 
eign countries throughout the period of human life with a degree 
of precision never before attained, so far as I am aware. It rep- 
resents the number of infants under one year as well as, and 
indeed better than, the number at middle life or advanced years ; 
and I cannot avoid the conviction that this formula affords an im- 
portant step toward the true mathematical expression of what we 
may call the life-curve. Modifications will doubtless be made in 
it ; indeed, it manifestly gives the numbers too small for the ages 
under 5 years, over 70 years, and between 20 and 45 years, while 
those of later childhood and youth on the one side, and of ad- 
vanced maturity on the other, are in excess. But the discor- 
dances are small, and I hardly think that any expression of equal 
simplicity will be found which will represent the life-curve more 
closely. 



AGES OF VOLUNTEERS. 33 

Of this formula, which is simply 

s n = a sin n k" 8 

where s n represents the sum of all under the age n, a is the total 
number, and k, 6 are two constants characteristic of the especial 
population under examination, details and applications are given 
in the Appendix ; where also are tables exhibiting the distribution 
of the total white male population of the United States and of the 
Loyal States, as given by this law. The values differ slightly from 
those in Tables XXI. and XXII., which, for the census of 1860 
at least, seem to be more accurate within the limits to which 
they are extended, although the corresponding numbers beyond 
these limits would be less accordant with observation. 



34 



AGES OF VOLUNTEERS. 



TABLE XX. 

White Male Population of the United States in 1860. 



Age 

at last 

birthday 



Actual Number 



15 

16 
17 
18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

2S 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 



At the 
given age. 



294 770 

289 680 

284 530 

279 320 

274 040 

268 700 

263 290 

257 820 

252 300 

246 720 

241 090 

235 380 

229 640 

223 840 

217 990 

212 090 

206 140 

200 140 

194 100 

188 020 

181 890 

175 710 

169 500 

163 250 

156 970 

150 640 

144 290 

137 900 

131 470 

125 020 

118 540 

112 030 

105 500 

98 940 

92 360 

85 760 



At aud o*ver 
given age. 



8 252 612 
7 957 842 
7 668 162 
7 383 632 
7 104 312 
6 830 272 
6 561 572 
6 298 282 
6 040 462 
5 788 162 
5 541 442 
5 300 352 
5 064 972 
4 835 332 
4 611 492 
4 393 502 
4 181 412 
3 975 272 
3 775 132 
3 581 032 
3 393 012 
3 211 122 
3 035 412 
2 865 912 
2 702 662 
2 545 692 
2 395 052 
250 762 
Iff 862 
981 392 
856 372 
737 832 
625 802 
520 302 
421 362 
329 002 



At and over 

given age and 

under 46. 



5 645 800 

5 366 480 

5 092 440 

4 823 740 

4 560 450 

4 302 630 

4 050 330 

3 803 610 

3 562 520 

3 327 140 

3 097 500 

873 660 

655 670 

443 5S0 

237 440 

037 300 

1 843 200 

1 655 180 

1 473 290 

1 297 580 

1 128 080 

964 830 

807 860 

657 220 

512 930 

375 030 

243 560 

118 540 



Relative Number 



At the 
given age. 



10 000 
9 811 
9 620 
9 426 
9 230 
9 033 
8 833 
8 631 
8 427 
8 222 
8 014 



804 
593 
380 
165 
949 
6 731 
6 512 
291 
068 
845 
620 
393 
166 
937 
707 
476 
244 
Oil 
777 
542 
307 
072 



At and over 
given age. 



10 000 
9 622 
9 251 

8 887 
8 530 
8 181 



839 
505 
179 
860 
549 
246 
951 
664 
385 
114 
851 
596 
350 
112 
882 
661 
448 
244 
049 
862 
684 
515 
354 
202 
059 
925 
800 



At and over 

given age & 

under 46. 



10 000 
9 505 
9 020 
8 544 

8 078 



621 
174 
737 
310 
893 
486 
090 
704 
328 
963 
609 
265 
932 
610 
299 
999 
1 710 
1 432 
1 165 
909 
665 
432 
210 



AGES OF VOLUNTEERS. 



35 



TABLE XXI. 

White Male Population of the Loyal States in 1860. 



Age 
at last 
birth- 
day. 


1 

At the 
given age. 


Lctual Numb 

At and over 
given age. 


er 

At and over 

given age 

and under 46. 


Re] 

At the 
given age. 


ative Num 

At and over 
given age. 


ber 

At and over 
jiven age & 
under 46- 


Prop to 
W. Male 
Pop. of 

United 
States. 


15 


228 120 


6 675 533 












7 739 


16 


225 270 


6 447 413 












7 776 


17 


222 280 


6 222 143 












7 812 


18 


219 160 


5 999 863 


4 574 220 


10 000 


10 000 


10 


000 


7 846 


19 


215 940 


5 780 703 


4 355 060 


9 853 


9 634 


9 


521 


7 880 


20 


212 600 


5 564 763 


4 139 120 


9 700 


9 275 


9 


049 


7 912 


21 


209 130 


5 352 163 


3 926 520 


9 542 


8 920 


8 


584 


7 943 


22 


205 550 


5 143 033 


3 717 390 


9 379 


8 572 


8 


127 


7 973 


23 


201 870 


4 937 483 


3 511 840 


9 211 


8 229 


7 


678 


8 001 


24 


198 070 


4 735 613 


3 309 970 


9 038 


7 893 


7 


237 


8 028 


25 


194 160 


4 537 543 


3 111 900 


8 859 


7 563 


6 


804 


8 054 


26 


190 150 


4 343 383 


2 917 740 


8 676 


7 239 


6 


379 


8 078 


27 


186 040 


4 153 233 


2 727 590 


' 8 488 


6 922 


5 


963 


8 101 


28 


181 820 


3 967 193 


2 541 550 


8 296 


6 612 


5 


555 


8 123 


29 


177 500 


3 785 373 


2 359 730 


8 099 


6 309 


5 


157 


8 141 


30 


173 100 


3 607 873 


2 182 230 


7 898 


6 013 


4 


769 


8 162 


31 


168 590 


3 434 773 


2 009 130 


7 692 


5 725 


4 


391 


8 179 


32 


163 990 


3 266 183 


1 840 540 


7 483 


5 444 


4 


022 


8 194 


33 


159 300 


3 102 193 


1 676 550 


7 269 


5 170 


3 


663 


8 207 


34 


154 530 


2 942 893 


1 517 250 


7 051 


4 905 


3 


315 


8 219 


35 


149 680 


2 788 363 


1 362 720 


6 829 


4 647 


2 


977 


8 229 


36 


144 730 


2 638 683 


1 213 040 


6 604 


4 398 


2 


650 


8 237 


37 


139 720 


2 493 953 


1 068 310 


6 375 


4 157 


2 


334 


8 243 


38 


134 620 


2 354 233 


928 590 


6 143 


3 924 


2 


029 


8 246 


39 


129 460 


2 219 613 


793 970 


5 907 


3 699 


1 


735 


8 247 


40 


124 230 


2 090 153 


664 510 


5 668 


3 484 


1 


452 


8 247 


41 


118 920 


1 965 923 


540 280 


5 426 


3 277 


1 


180 


8 242 


42 


113 550 


1 847 003 


421 360 


5 181 


3 078 




920 


8 234 


43 


108 110 


1 733 453 


307 810 


4 933 


2 889 




672 


8 223 


44 


102 620 


1 625 343 


199 700 


4 683 


2 709 




436 


8 209 


45 


97 080. 


1 522 723 


97 080 


4 430 


2 538 




212 


8 190 


46 


91 480 


1 425 643 




4 174 


2 376 






8 165 


47 


•85 830 


1 334 163 




3 916 


2 224 






8 136 


48 


80 130 


1 248 333 




3 656 


2 081 






8 099 


49 


74 400 


1 168 203 




3 394 


1 947 






8 055 


50 


68 640 


1 093 803 




3 130 


1 823 






8 001 



36 AGES OF VOLUNTEERS. 

The results present some curious contrasts between the life- 
curves for the total population in the loyal States and in the 
insurgent States, which may be best recognized by reference to 
the appended chart, marked E. This chart exhibits the number 
of white males at each year of age from 18 to 50, corresponding 
to each 10 000 at the age of 18. It will be seen at once that the 
curvature of the line representing the population of the insurgent 
States is in the direction opposite to that of the lines belonging 
to the loyal States and to the whole country. The dotted line 
is straight, and shows what the distribution would be, did it follow 
a regular arithmetical progression. To what extent this differ- 
ence may be due to immigration from Europe, which has been 
chiefly to the Free States, I will not undertake to estimate. We 
have seen, however, that the law of distribution of our volunteer 
troops according to ages was essentially the same for those States 
to which immigration is ■ greatest as for those to which it is 
least. 



The construction of all the curves laid down on the accompany- 
ing charts will be manifest without explanation. For those or- 
dinates which belong to the respective ages they give the corre- 
sponding numbers. 



APPENDIX. 



ON THE AGES OF A POPULATION. 

In the course of the preceding investigation, the interesting question as 
to the general distribution of a population by ages became prominent ; and 
the inquiry continually suggested itself, how far any simple formula might 
be capable of representing the observed numbers for all ages of life. This 
has incidentally led to the detection of what seems to be the true law, which, 
although not strictly pertaining to the subject in hand, seems yet to possess 
sufficient practical value and importance in its indirect bearing to justify its 
introduction here, — the more especially, since endeavors to obtain informa- 
tion on this point elsewhere have proved fruitless. 

It appears that, in a population at all homogeneous in its character, the 
number of persons under the age n years may be represented by the simple 
expression 

N= a sin n k n 6 

in which a denotes the total number of the population, while k and 6 are 
constants peculiar to the country and epoch. The quantity 6 is an angle 
somewhat larger than 1°, and k is a number, generally a little less than 
unity. 

For the special case &= 1, the formula becomes 

iV= a sin n 8 

containing only one unknown quantity, the angle 6, to be determined by 
investigation. 

A very peculiar characteristic of this law is recognizable in the circum- 
stance that the number at any given age appears to be strictly proportional 
to the whole population ; so that the expectation of life, for the average indi- 
vidual, is as well represented as is the general distribution by ages of the 
total number of individuals, of whom the population is composed. 



38 AGES OF VOLUNTEERS. 

Investigating the values of the constants k and 6 for the people of the 
United States at each of the last four enumerations, we find 

Date k 6 

1830 0.9918 2°.0524 

1840 0.9921 1°.9747 

1850 0.9932 1°.8361 

1860 0.9941 1°.7307. 

The census of 1820 is not sufficiently distinct, in the assortment by ages, 
to permit a determination of the constants, but the indications are clear 
that a proper enumeration would have afforded results in conformity with 
the preceding series ; the value of k being smaller, and that of 6 larger than 
for the population in 1830. 

The curious fact thus becomes evident, that our population has, during 
the last forty years or more, been gradually assimilating itself to the normal 
type represented by k = 1 ; growing, or developing itself, so to speak, 
toward a compliance with the simple law 

iV= a sin n 6 

in which the value of 6 indicates the longevity of the people, since, accord- 
ing to the formula, the entire population becomes extinct at the age when 
nd=90°. 

How far immigration has affected the values of the constants for the 
United States we will not now inquire. Were the tendency to immigrate 
independent of age, no appreciable influence could be traced to this source ; 
and the character of the immigration into this country seems to have been 
such as to exhibit no great preponderance or deficiency for any one period of 
life, except perhaps that there is some deficiency in the relative number at 
the most advanced ages. But the accessions to our population from Ireland 
and Germany appear to have been in most cases by families, and not com- 
posed chiefly of persons in the prime of life or fullness of strength, as is the 
case in very new countries. 

The English people appearing to afford a fair specimen of a permanent 
and normal population, the last two censuses of England and Wales were 
examined, and with the following result : — 



Date 


k 


6 


1851 


0.9957 


1°.4702 


1861 


0.9962 


1°.4316. 



Thus a similar phenomenon is manifested by the English enumeratibns to 
that exhibited by the American census-returns ; the values of k approach- 
ing unity, and those of 6 diminishing. The smaller value of the angle 6 



AGES OF VOLUNTEERS. 39 

indicates a longer duration of life in that country ; but k, the modulus of 
the change by geometric progression, was not larger for England in 1851 
than it bids fair to be for the United States in ten years from the present 
time. 

Passing next to the French population, we find the value k = 1 as the 
result alike of the last three enumerations, the values of 6 being 



in 1851 


1°.0553 


" 1856 


1°.0556 


" 1861 


1°.0473. 



The remarkable peculiarity of the life-curve for France, as regards the 
small infantile mortality, is well exhibited by the chart F, which shows 
the number living, at,each year of age, for every million in the population. 
The several curves of this chart represent the distribution of ages for the 
United States in 1830 and 1860, (those for the intermediate decades being 
omitted to avoid confusion,) for England in 1861, and for France. The 
English curve for 1851 would differ too slightly from that for 1861 to be 
conveniently distinguished on the chart; and the French curves for 1851, 
1856, and 1861 would be undistinguishable from one another. 

The chart G shows the corresponding values of N, (the number under 
each year of age,) for each nation, and clearly manifests the differences in 
the law, corresponding to the diversity in the constants. 

The tables of population deduced from the census-returns already cited, 
together with the values given by the formula, are here appended, reduced 
however, in each case, to the scale of one million of population. The dif- 
ferences are given in decimals of the census-numbers, and the accordance 
between the formula and the recorded numbers will be manifest at the first 
inspection. The chief discrepancies will be found in the French tables, for 
the ages 

exceeding 50, in the census of 1851 
« 55, " " " " 1856 
" 60, " " " " 1861. 

This curious circumstance and the nature of the discordances suggest some 
historical explanation ; which the disturbed condition of the French nation 
at the period corresponding to the birth of this portion of the population 
seems to render plausible. 



40 



AGES OF VOLUNTEERS. 



TABLE XXII. 

Ages of the Population of the United States, 
as deduced from the Census Returns of 1830 and 1840. 



AGE. 


Census of 1830. 


Census of 1840. 


Proportions 
Observed. 


tl numbers. 
Calculated. 


Difference. 
(C.-O.) 


Proportion 
Observed. 


il numbers. 
Calculated. 


Difference. 
(C-O.) 


0- 5 


17977 


17082 


-0.050 


17437 


16334 


-0.063 


5-10 


14576 


15254 


+0.046 


14173 


14651 


+0.034 


10- 15 


12452 


13280 


+0.014 


12094 


12931 


+0.069 


15 - 20 


11147 


11318 


+0.024 


10911 


11205 


+0-027 


20-30 


17752 


17244 


-0.029 


18155 


17456 


-0.038 


30-40 


10908 


11287 


+0.035 


11597 


11790 


+0.017 


40 - 50 


6886 


6932 


+0.007 


7320 


7466 


+0.020 


50-60 


4308 


3973 


-0.078 


4365 


4389 


+0.005 


60-70 


2525 


2100 


-0.168 


2449 


2343 


-0.043 


70-80 


1104 


992 


-0.100 


1132 


1067 


-0.058 


80 & over 


365 


540 




367 


368 





TABLE XXIII. 

Ages of the Population of the United States, 
as deduced from the Census Returns of 1850 and 1860. 



AGE. 


Census of 1850. 


Census of 1860. 


Proportion; 
Observed. 


il numbers. 
Calculated. 


Difference. 
(C.-O.) 


Proportion) 
Observed. 


il numbers. 
Calculated. 


Difference. 
(C.-O.) 


0- 1 


2751 


3170 


+0.152 


2998 


3003 


+0.002 


1-5 


12070 


12215 


+0.012 


12300 


11608 


-0.056 


5-10 


13836 


14102 


+0.019 


13117 


13484 


+0.028 


10- 15 


12292 


12564 


+0.022 


11588 


12206 


+0.053 


15-20 


10892 


10990 


+0.009 


10625 


10853 


+0.021 


20-30 


18562 


17505 


-0.057 


18242 


17692 


-0.030 


30-40 


12368 


12225 


-0.012 


13012 


12760 


-0.019 


40-50 


8130 


8019 


-0.013 


8496 


8618 


+0.014 


50-60 


4903 


4883 


-0.041 


5214 


5366 


+0.029 


60-70 


2667 


2695 


+0.010 


2910 


2953 


+0.015 


70-80 


1147 


1250 


+0.090 


1158 


1261 


+0.089 


80 & over 


382 


382 




340 


196 





AGES OF VOLUNTEERS. 



41 



TABLE XXIV. 

Ages of the Population of England and Wales, 
as deduced from the Census Returns of 1851 and 1861. 



AGE. 


Census of 1851. 


Census of 1861. 


Proportion 
Observed 


il numbers. 
Calculated. 


Difference. 
(C. - O.) 


Proportion! 
Observed. 


il numbers. 
Calculated. 


Difference. 
(C. - O.) 


0- 5 


13006 


12533 


-0.035 


13352 


12245 


-0.083 


5-10 


11590 


11800 


+0.018 


11588 


11575 


-0.001 


10-15 


10616 


10987 


+0.034 


10415 


10819 


+0.040 


15-20 


9832 


10079 


+0.013 


9688 


10007 


+0.032 


20-25 


9441 


9114 


-0.036 


9317 


9108 


-0.023 


25-30 


8307 


8170 


-0.017 


7932 


8178 


+0.030 


30-35 


7168 


7179 


+0.004 


6950 


7282 


+0.046 


35-40 


6083 


7273 


+0.030 


6111 


6352 


+0.038 


40-45 


5393 


5378 


-0.003 


5638 


5506 


-0.024 


45-50 


4440 


4546 


+0.023 


4617 


4705 


+0.019 


50-55 


3934 


'3782 


-0.040 


3995 


3820 


-0.046 


55-60 


2919 


3061 


+0.046 


3039 


3245 


+0.063 


60-65 


2668 


2426 


-0.100 


2751 


2512 


-0.095 


65-70 


1815 


1841 


+0.014 


1862 


1910 


+0.025 


70-75 


1386 


1332 


-0.041 


1391 


1355 


-0.026 


75-80 


809 


876 


+0.076 


794 


869 


+0.086 


80-85 


410 


481 


+0.173 


394 


435 


+0.104 


85 & over. 


183 


142 




146 


77 




Total, 


100000 


100000 




100000 


100000 





FORMULAS 

For 1851, JST= 100 000 sin n (0.99575)" . 1°.4702. 
1861, IT= 100 000 sin n (0.99616)" . 1°.4316. 



6 



42 



AGES OF VOLUNTEERS. 



TABLE XXV. 

Ages of the Population of France, 
as deduced from the Census Returns of 1851, 1856, and 1861. 



AGE. 



0- 
5- 
10- 
15- 
20- 
25- 
30- 
35- 
40- 
45- 
50- 
55- 
60- 
65 
70- 
75 
80 
85 J 



5 

10 
15 
20 
25 
•30 
35 

■ 10 
45 

■ 50 

■ 55 
■60 
•65 
-70 
-75 
-80 
-85 

i over. 



Census of 1851. 



Proportional 
numbers. 

Ob- Caleu- 
served. lated. 



Total, 



9291 
9216 
8800 
8805 
8326 
8020 
7565 
7188 
6596 
5S69 
5782 
4390 
3670 
2785 
1952 
1062 
480 
203 

100000 



Difference. 
(C.-O.) 



9208 
9130 
8946 
8716 
8437 
8036 
7616 
7105 
6534 
5890 
5233 
4512 
3753 
2954 
2148 
1313 
468 
1 

100000 



-0.009 
-0.009 
+0.016 
-0.010 
+0.013 
+0.002 
+0.007 
-0.012 
-0.009 
+0.004 
-0.095 
+0.028 
+0.023 
+0.059 
+0.100 
+0.239 
-0.025 



Census of 1856. 



Proportional 
numbers. 



Ob- 
served. 



9568 
9120 
8821 
8530 
8077 
8075 
7575 
7255 
6656 
6041 
5317 
4838 
3734 
2757 
1902 
1088 
453 
193 

100000 



Calcu- 
lated. 



Difference. 
(C - O.) 



9200 
9119 
8965 
8736 
8427 
8051 
7614 
7092 
6526 
5902 
5228 
4503 
3753 
2958 
2145 
1312 
468 
1 

100000 



-0.038 
0.000 
+0.016 
+0.024 
+0.043 
-0.003 
+0.005 
-0.022 
-0.020 
-0.023 
-0.017 
-0.069 
+0.005 
+0.076 
+0.128 
+0.205 
-0.033 



Census of 1861. 



Proportional 
numbers. 

Ob- Calcu- 

served. lated. 



9677 
8767 
8668 
8701 
8237 
7857 
7421 
7098 
6625 
6155 
5382 
4559 
4160 
2941 
1940 
1123 
490 
199 

100000 



Difference. 
(0. - 0.) 



9124 
9052 
8898 
8722 
8374 
8005 
7564 
7071 
6514 
5900 
5254 
4518 
3790 
3016 
2218 
1398 
568 
14 

100000 



-0.088 
+0.032 
+0.027 
+0.002 
+0.017 
+0.019 
+0.019 
-0.004 
-0.017 
-0.041 
-0.024 
-0.009 
-0.090 
+0.025 
+0.143 
+0.245 
+0.159 



FORMULAS 

For 1851, N= 100 000 sin n (1°.0553). 
1856, N= 100 000 sin n (1°.0556). 
1861, N= 100 000 sin n (1°.0473). 



AGES OF VOLUNTEERS. 43 

The agreement of the observed numbers with those given by our formula 
is indicated by the quantities in the columns headed G. — 0. (i. e. Com- 
puted minus Observed), and appears to be entirely within the limits of 
probable error in the enumeration, — if we except those discordances for 
the French census already alluded to. It affords a strong argument for 
belief that the true form of the normal life-curve is closely represented 
by the sine-formula. 

The only other statistics of ages for European populations, which have 
been conveniently accessible, are contained in the abstract of the Prussian 
census of 1852, given by Brachelli, in the second volume of his Deutsche 
Staatenkunde. A discussion of the numbers there recorded gives 

jfe = 0.9960, 0=1°.47O2, 

these values being closely similar to those for England and Wales in 
1851. 

It is manifest that if the number under any given age n be represented 
by the expression 

N = a sin n k 71 8 

the number between the ages n and n-\-\ will be expressed by 

2a sin ^kf 1 (kn-\-k — n)6. cos ^k 71 (k n -\- k -{- n) 6, 

and the mortality at the same period, by the finite difference of this quantity. 
But when 6 becomes unity, these values are greatly simplified, and we 
have 

Population under the age n years = a sin n 6 

Population at " " " " = 2a sin \6 cos (n-\- ±)d 

Mortality " " « " " = 4 a sin (n + 1) 6 sin 2 \6. 

According to the formula here presented, the life-curve for advanced ages 
bears no similarity to an asymptote, but ceases abruptly when the quantity 

90° 
n k"6 = 90° ; or for the case of k = 1, when n = - . This indicates that 

8 

all ages above this limit are exceptional, and to be regarded in the same 
light as deviations from the theoretical number at other periods of life. 

The many paths of research offered by the residual discordances from 
the formula must be passed by on this occasion, with the single remark that 
they offer indications of abundant reward for any explorer. 

It is proper to add, that in these investigations, as in those on the Ages of 
Volunteers, the computations have been almost exclusively carried on by 
Mr. J. N. Stockwell. 



Cambridge, January, 1866. 



Thonsi 

^frUt A. 

*i //f'ftrf//'f/(/r f/te /'( /<///<>// 

z Jed and/wmputed namdc/w. 



represent the recorded numbers i 
■>l(? are computed. Those for officers 
i, for greater distinctness. ) 



22< 



•ion 



IM 



IttO 













































140 














































































G&O 
















































































I«KI 
















































































SO 




















































































<)() 
















































































K» 


















































































20 
















































- 



















r === 


-:- 










\.$e, IS 


+ 


» + 


i 


+ 


■» t 


i 4 


+ 


S 


t- 


Years. 



Chant Ji. 

Exhibiting fortach year #f age f/te relation 
oetmxn the recorded andjcomputed numbers, 
of volunteers. 

(The dotted lines represenl the recorded numbers) 
Ulp contimioua oneg are computed. Those for officers 
are multiplied by ten, for greater distinctness.) 




Ave. ik |,q 20 ii i'i 23 2* ' i6 2<i 



2« T. M 



).) 30 31 32 33 34 35 36 .17 38 



39 40 +t te +•> ** H S6 



17 W 10 V»'.l 



Xiimlifi 



10,00(1 




















\ 






\ 


9.000 






















A 








\ 












,S.O(ll> 
























V 










v., 










\\ 




7.UIIO 


























K 










\\ 


OOOO 








\^, 




































5,000 






































tpoo 
















































.'l.itOO 































































































































































Age 18 l!» 20 „'i 2 



XiiiiiImT 



10,0 CM 










>r,. 












L/iart //. 
























.)/*//> •///,/ //*,- re/afire tuimter 0/' 






























, 


population of mi/ifari/ /?///> ,//„>„/ 




































O) rr ff////fpY//-o/Vu/r/ro/// M/o /->', 






Y 






















<- 




fTI.,. ,!„»-... 1 l: !..JJ- . .1 1 1 


8,000 










1 1111 ii.M.r.i lilies IIKMCIle MIC ITCOnlCd IIHIIllXTS 


















£5, 






the continuous lilies thiToiiiuiiteil ones.) 




































\ -. 














\\ 




















7,000 



























































































































- 








































































— 








- 








V, 


























\ 


























































5,000 




































































































































































































tDOO 
















































































































<x 














































































s'C 














["> 


































\. 1 
















£ 
































V^r 














'"*■ 






































s* 














-t> 




































^ 












\^s 








































s^jfe 












So 


'sT 










aooo 






























































































\^i 






















































^ 


























































5^ 






























































































































































































































































































































1 














Lz 










J_J 


. 


1 








1 






1 1 1 1 1 1 



Age 18 19 20 ii 22 23 24 25 26 27 28 29 30 



31 .12 33 ;<4 35 36 37 38 if) -to U 42 -f;i 44 (.'. Yearn 



Number 













- 




^: 


































































6000 






















_Jl 










-■- 




j 








■• 
















— 


— 


























6.000 
















































5000 
















































4000 












































































































2,000 






















































~~i 


# 


[ 



















A%e IS ID i0 U 



1000 



aooo 



2,000 



CAart C 

ExkiditingJbreacA year of age tAenum- 
bn •»/ >//// ?ted men and officers among Mr 
first million i vlnnteers, and ihe number 
o/t i hilt males in ^population WWi/offhr 
/ hi ted . S Votes andqftAe loyal ■ S inte »-. 

The doited lines are straight. The number 
of officers is multiplied by ten for distinctness. 




M<~ W 19 20 21 22 23 2* 25 26 27 28 2? 



.11 32 ;5.'l 3# 3* ;J6 •' 17 ;,H ~'> *° M K 13 ^ M ffl W *fl W ■'>•• Ve.'i* 



Numbej 
10,000 



•1000 



80(10 



7001) 



('hurt /). 
ShoH /'//{/ /or ////// r.sf > vhtatfn x. the n///o of 
tffieexs&mtn /»//// n -hifc male populatwn 
qfithe loyal states at the same ages. 
• (Thenumber of officers is multiplied byten.) 



toon 



aooo 



lOOO 




A§e 18 ; li 20 21 22 83 2* 25 2« 27 28 2!) .10 31 32 33 34 



3,5 .16 37 -IK 38 Wi H VI 43 44 f"> Yc.ir.s. 



Number 

10,000 
















J^5 


^> 


;— 












9,000 


























































8,000 
























































r.iiiio 


























































6000 


























































5,000 


























































4,000 


























































.1,000 


























































2,000 


























































L0O0 





































































Aye 18 19 20 21 



; 



Number 



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4- 
































































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